Simplify to lowest terms. $\dfrac{36}{27}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 36 and 27? $36 = 2\cdot2\cdot3\cdot3$ $27 = 3\cdot3\cdot3$ $\mbox{GCD}(36, 27) = 3\cdot3 = 9$ $\dfrac{36}{27} = \dfrac{4 \cdot 9}{ 3\cdot 9}$ $\hphantom{\dfrac{36}{27}} = \dfrac{4}{3} \cdot \dfrac{9}{9}$ $\hphantom{\dfrac{36}{27}} = \dfrac{4}{3} \cdot 1$ $\hphantom{\dfrac{36}{27}} = \dfrac{4}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{36}{27}= \dfrac{3\cdot12}{3\cdot9}= \dfrac{3\cdot 3\cdot4}{3\cdot 3\cdot3}= \dfrac{4}{3}$